Recording Details

Abstract

We discuss well-posed initial-boundary value formulationsin general relativity. These formulations allow us to construct solutions ofEinstein's field equations inside a cylindrical region, given suitable initialand boundary data. We analyze the restrictions on the boundary data that resultfrom the requirement of constraint propagation and the minimization of spuriousreflections, and choosing harmonic coordinates we show how to cast the probleminto well-posed form. Then, we consider the particular case where the boundaryrepresents null infinity of an asymptotically flat spacetime. Here, the rôle ofthe boundary conditions is to provide adequate regularity and gauge conditionsat infinity.

As an application of our setup we mention ongoing work onthe computation of quasi-stationary scalar field configurations on anon-rotating supermassive black hole background.